The published foundations of TFPT

HYP.FIBER.01Construction [E]/[C] (fibered substrate)

HYP.REWRITE.01Construction/proof [E]/[O] (cusp weight from a minimal rewrite)

DYNAMICS.UNIVERSAL.01Universal synthesis [E]/[C] (every sector = a gapped operator with a unique attractor + spectral gap => parameter-free; extends v303 theory-wide; 3 gaps computed, the cross-sector identification [C])

CORRECTIONS.GAP.01Correction calculus [E]/[C] (each sector's gap sets its first-correction size; (2/3)^6 family vs golden family; the harvest of v383)

COXETER.PRIME2.01Prime-2 facet of the Coxeter clock [E]/[C] (h(E8)=30=2*3*5; one quadratic facet field per prime, ramified at it; the prime-2/Gaussian/Z4-seam facet completes v383's golden and family facets)

FORM.SPECTRALGAP.01Formal [F] (Lean kernel; no extra axioms) -- the scalar core + the finite-dimensional diagonalisable case of the spectral-gap meta-theorem (v383): gap => unique attractor + geometric decay => parameter-free

COXETER.ATOMS.01Clockwork coherence [E]/[C] (Coxeter primes = anchor atoms = facet fields; chi=3^6/(3^6-2^6); both dynamic rates carry prime-2; 30=5x6) -- a bird's-eye re-reading, no new number

HYP.COUPLED.01Coupled hypergraph rewrite [E]/[O] (one local rule unifies carrier x family; joint attractor marks x e0; recovery (2/3)^6 after one hand; v324 fiber emerges as cusp readout; v299 growth unchanged) -- mechanism unified, phi0 + seed remain

RES.COXETER.SYMMETRY.01Structural lemma [E]/[C] (prime-2 necessary, not autonomous: the sheet involution has spectrum {+-1} and projector {0,1}, none in (0,1), so no prime-2-only attractor; reuses established atoms, no new number) -- closes the v394 open-question corollary

E8.CMDUAL.01E8 character CM-duality [E]/[C] (chi_E8(i)=12 vs chi_E8(omega)=0: the (E8)_1 character maximal at the seam tau=i, zero at the family tau=omega; the two are the only elliptic points so the values are forced) -- the seam/flavor rigidity duality, extends v282

SEAM.EQUIV.02Dual keystone at tau=omega [E]/[C]/[O] (the family/flavor sector as the order-3 Eisenstein/A2 face: chi_E8(omega)=0, A2 Cartan det 3=N_fam reads R in E6xA2 with det R=8=dim A2, delta=the tau=omega CM phase, cusp weights=the order-3 deck; dual to the seam=(E8)_1 at tau=i). A named contract, NOT a closure

FLAV.PMNS.CLOSE.01PMNS closed modulo the keystone [E]/[C]/[O] (CP-phase origin = the tau=omega CM phase v405; angles [E]; J=-0.0297 derived; absolute scale = one seesaw ratio = v_geo; zero free flavor dials beyond v_geo). Resolves v270's open phase + scale

FLAV.SELECTOR.CLOSE.01R4' selector folds into the keystone [E]/[C]/[O] (the (d,n) pairings {2,8,121}={|Z2|, rank E8=dim A2=det R, ||Pl(K)||_1^2} are the tau=omega family-slice atoms; n.a=8=dim A2 reads R in E6xA2; deriving (d,n) folds into SEAM.EQUIV.02; residue = why 11)

ARITH.TRICHOTOMY.01Atom trichotomy [E]/[C]: {2,3,5} ram/inert/split in Z[i] (2 ram, 3 inert, 5 split) vs Z[omega] (3 ram, 2,5 inert); the ramified prime of each ring = its atom; each atom is the unique ramified prime of one facet of Q(i,sqrt-3,sqrt5), product 30=h(E8); seam/flavor/golden reading [C]

DIAMOND.EISEN.01Eisenstein/CP operator [E]/[C]: the family rotation P realises the hex norm 7=N_omega(3+2omega) via (3I+2P)(3I+2P^2)={7,7,25} (dual of v415's {13,13,9}); the CP clock W=-P^2 (W^2=P, W^3=-I, Spec {-1,zeta6,zeta6^-1}) gives delta_CKM=pi/3, delta_PMNS=4pi/3; all flavor clocks are zeta30-powers, the seam mu4 the Galois side phi(30)=8=rank E8; the carrier mu5 has no 3x3 operator [C]

SEAM.GALOIS.01Seam mu4 = carrier's Galois group [E]/[C]: 30 squarefree => no order-4 cyclic, so the seam mu4 is the Galois side (Z/30)^x=mu4 x Z2; the mu4 factor IS (Z/5)^x=Gal(Q(zeta5)) (carrier), the Z2 IS (Z/3)^x (family/CP); the Frobenius zeta5->zeta5^2 is the explicit order-4 operator G with G C5 G^-1=C5^2, G^4=I; resolves the v409 asymmetry (seam = automorphism, not a hand) [C]

GRAV.ENTROPIC.SCALEFLOW.01Formal/Identity [E] (scale-flow + moment dictionary + closure identity, exact) + [C] (measure is TFPT input) + [O] (R^2 gate unchanged)

FLAV.NUSCALE.02Candidate [P]/[N]/[X]/[C]/[O] (carrier normalisation collapses the trade-off; window bracketing; integer rung declined at 1-loop; decision computation named)

HYP.REWRITE.02Construction/uniqueness [E]/[O] (full spectrum from the unique lazy Z2-pair walk; split selection stays open)

FLAV.NUSCALE.04Enumeration/decision [E]/[O] (the 3/5 Clebsch door closed; negative result; window candidate stands)